Question

Arlington Manufacturing is contemplating replacing one of its machines with a new, more efficient machine. The old machine is being depreciated on a straight-line basis over the next 5 years. It has a book value of $200,000 and could be sold for $120,000. The replacement machine would cost $600,000 and have an expected life of 5 years, after which it could be sold for $100,000. Because of reductions in defects and material savings, the new machine would produce cash benefits of $180,000 per year before depreciation and taxes. The present value of $1 at 15% received after 5 periods at 15% is 0.49718. The present value of an annuity of $1 for 4 periods at 15% is 2.85498, and for 5 periods is 3.35216. Assuming straight-line depreciation, a 40% marginal state and federal tax rate, and a required rate of return of 15%, find the payback period and NPV.

Answer 1

		a	Initial Cash Flow:
			Before tax sallvage value of old machine	$120,000
			Book value of old machine	$200,000
			Gain on Salvage=200000-120000=	$80,000
			Tax on gain =80000*40%	$32,000
		A	After tax salvage value of old machine	$88,000	(120000-32000)
		B	Cost of replacement machine	($600,000)
		C=A+B	Initial Cash Flow:	($512,000)
			DEPRECIATION OF OLD MACHINE
			Year from today	1	2	3	4	5
		D1	Annual Depreciation expense=200000/5=	$40,000	$40,000	$40,000	$40,000	$40,000
			DEPRECIATION OF NEW MACHINE
			Year(from today)	1	2	3	4	5
		D2	Annual Depreciation expense=(600000-100000)/5	$100,000	$100,000	$100,000	$100,000	$100,000
		D=D2-D1	Change in annual depreciation expense	$60,000	$60,000	$60,000	$60,000	$60,000
		N	Year From Today	1	2	3	4	5
		E=D*40%	Depreciation tax shield	$24,000	$24,000	$24,000	$24,000	$24,000
		F	Before tax saving in operating cost	$180,000	$180,000	$180,000	$180,000	$180,000
		G=F*(1-0.4)	After tax increase in operating cash flow	$108,000	$108,000	$108,000	$108,000	$108,000
		H	Salvage value					$100,000
		I=E+G+H	Incremental Net Cash Flow	$132,000	$132,000	$132,000	$132,000	$232,000
			Cumulative cash flow
		J	Present Value of Year1-4 Cash Flows	$376,857	(2.85498*132000)
		K	Present Value of Year 5 Cash Flows	$115,346	(0.49718*232000)
		L=J+K	Present Value of Cash Inflows	$492,203
		I	Sumof Present Value of Cash outflow	-$512,000
		NPV=L+I	Net Present value	($19,797)
			NPV is Negative
			No, the machine should NOT be purchased
			Payback Period=512000/132000=	3.88	Years